Mr. Adams,
I have a book, Roster of our Dead Buried in Confederate Cemetery at Chattanooga, TN, and did not find an Adams from GA listed buried there. However, there is a mass grave there and your Adams' could be there. There is also a Confederate Cemetery on Lee Hwy in Chattanooga, Silverdale Confederate Cemetery, where 155 Unknown Confederates are buried who died in area hospitals.
Take care and best of luck in your research endeavors,
Joanie